In a large mixing bowl, beat together butter and sugar.
Add egg, milk and vanilla, mix well.
In a separate bowl, whisk together flour, cocoa powder, baking soda and salt.
Add flour mixture to butter mixture,stirring with spoon until well combined and no more dry patches.
Refrigerate dough for 1 -2 hours or until chilled and firm enough to handle. Dough will be a little soft.
Preheat oven to 350°F. Lightly grease cookie sheet or line with parchment paper.
Scoop out tablespoon of cookie dough. Roll dough into a ball. Flatten slightly and press peppermint patty into dough. Mold dough around patty so that it is completely covered. It's important that the patty is completely covered - it will melt and ooze out if it's not.
Place on prepared cookie sheet.
Bake for about 12 minutes or until cookie is set.
Let cookie rest for a minute or two on cookie sheet and carefully transfer to wire rack. Cool completely. Store in sealed container.
Makes approximately 18 cookies.